High locality and increased intra-node parallelism for solving finite element models on GPUs by novel element-by-element implementation

The utilization of Graphical Processing Units (GPUs) for the element-by-element (EbE) finite element method (FEM) is demonstrated. EbE FEM is a long known technique, by which a conjugate gradient (CG) type iterative solution scheme can be entirely decomposed into computations on the element level, i.e., without assembling the global system matrix. In our implementation, NVIDIA´s parallel computing solution, the Compute Unified Device Architecture (CUDA), is used to perform the required element-wise computations in parallel. Since element matrices need not be stored, the memory requirement can be kept extremely low. It is shown that this low-storage but computation-intensive technique is better suited for GPUs than those requiring the massive manipulation of large data sets. This study of the proposed parallel model illustrates a highly improved locality and minimization of data movement, which could also significantly reduce energy consumption in other heterogeneous HPC architectures.